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HMMT 十一月 2024 · 冲刺赛 · 第 22 题

HMMT November 2024 — Guts Round — Problem 22

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [12] Suppose that a and b are positive integers such that gcd( a − b , ( a − b ) ) is not divisible by any perfect square except 1 . Given that 1 ≤ a − b ≤ 50 , compute the number of possible values of a − b across all such a, b . ̂
解析
  1. [12] Suppose that a and b are positive integers such that gcd( a − b , ( a − b ) ) is not divisible by any perfect square except 1. Given that 1 ≤ a − b ≤ 50 , compute the number of possible values of a − b across all such a, b . Proposed by: Srinivas Arun Answer: 23 Solution: Recall that a positive integer is squarefree if it is not divisible by any perfect square except